Question

A body oscillates with SHM, accroding to the equation, `x=(5.0m)cos[(2pi t+pi//4]`
At `t=1.5s`, calculate the `(a)` diplacement `(b)` speed and `(c)` acceleration of the body.

Answer 1

Here, `omega =2pira//s,`
`T=(2pi)/(omega)=(2pi)/(2pi)=1s,t=1.5s`
`(a)` displacement,
`s=(5.0)cos[2pixx1.5+pi//4]`
`=5.0cos(3pi+pi//4)=-5.0cospi//4`
=-5.0xx0.707=-3.535m
`(b)` speed, `v=(dx)/(dt)`
`=-5.0xx2pisin(2pit+pi//4)`
`=-5.0xx2pisin(2pixx1.5+pi//4)`
`=5.0xx2pixxsin((pi)/(4))=5.0xx2xx(22)/(7)xx0.707`
`=22.22ms^(-1)`
`(c)` Acceleration ` A=(dv)/(dt)`
`=-5.0xx4pi^(2)cos(2pit+(pi)/(4))`
`=-5.0xx4xx((22)/(7))^(2)xxxx0.707=139.56ms^(-2)`